0 Transfer Matrices and Partition - Function Zeros for Antiferromagnetic Potts Models II . Extended results for square - lattice chromatic polynomial
نویسندگان
چکیده
We study the chromatic polynomials for m × n square-lattice strips, of width 9 ≤ m ≤ 13 (with periodic boundary conditions) and arbitrary length n (with free boundary conditions). We have used a transfer matrix approach that allowed us also to extract the limiting curves when n → ∞. In this limit we have also obtained the isolated limiting points for these square-lattice strips and checked some conjectures related to the Beraha numbers.
منابع مشابه
Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models IV. Chromatic polynomial with cyclic boundary conditions
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متن کاملSe p 20 01 Transfer Matrices and Partition - Function Zeros for Antiferromagnetic Potts Models
We study the chromatic polynomials for m × n square-lattice strips, of width 9 ≤ m ≤ 13 (with periodic boundary conditions) and arbitrary length n (with free boundary conditions). We have used a transfer matrix approach that allowed us also to extract the limiting curves when n → ∞. In this limit we have also obtained the isolated limiting points for these square-lattice strips and checked some...
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We study the chromatic polynomial PG(q) for m×n triangular-lattice strips of widths m ≤ 12P, 9F (with periodic or free transverse boundary conditions, respectively) and arbitrary lengths n (with free longitudinal boundary conditions). The chromatic polynomial gives the zero-temperature limit of the partition function for the q-state Potts antiferromagnet. We compute the transfer matrix for such...
متن کاملA pr 2 00 3 Transfer Matrices and Partition - Function Zeros for Antiferromagnetic Potts Models III . Triangular - lattice chromatic polynomial
We study the chromatic polynomial PG(q) for m×n triangular-lattice strips of widths m ≤ 12P, 9F (with periodic or free transverse boundary conditions, respectively) and arbitrary lengths n (with free longitudinal boundary conditions). The chromatic polynomial gives the zero-temperature limit of the partition function for the q-state Potts antiferromagnet. We compute the transfer matrix for such...
متن کاملTransfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models V. Further Results for the Square-Lattice Chromatic Polynomial
We derive some new structural results for the transfer matrix of squarelattice Potts models with free and cylindrical boundary conditions. In particular, we obtain explicit closed-form expressions for the dominant (at large |q|) diagonal entry in the transfer matrix, for arbitrary widths m, as the solution of a special one-dimensional polymer model. We also obtain the large-q expansion of the b...
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